Big Idea:
Students match graphs to equations and use these match-ups to create their own generalizations about how the parameters a, b and c affect the graph of the function y=a/(x-b)+c.

It is essential that students take the time to fully understand their answers to the first question on the warm-up. Sample_Answers are included below. The justification following “because” in each sentence is very important, and worth taking the time to discuss with each student. It is also important that students can visually see how these explanations relate to the asymptotes.

Note that for students who are struggling with these, you can provide a copy of the answers. The point is that they understand them, not that they generate them on their own. For students who struggle, I give them the answers and ask them to tell me which parts do and don’t make sense.

The second question is review from yesterday’s lesson and again it is important to ask students to take the time to complete at least the input sections of the data tables. For some of my students, it is tedious to fill out the outputs of the data tables because they already know what will happen, so it isn’t worth the time. For students who still haven’t figured out the approach statements, obviously it is important that they do this.

The back of the warm-up is great for students who have easily mastered the first two skills. By this time, many of my students have an easy time with the first page, so the challenge is possible in the 30 minutes.

Resources

This Exit Ticket is basically asking students to extend the ideas that they developed today. Already with their partner, they have produced a write-up explain how the parameters a, b, and c affect the function’s graph. With these questions I ask my students to consider how changes to the equation affect the graph. It isn’t necessary for students to write everything down; the write-ups are provided as an example, but students will be more likely to think about these questions if they just need to discuss them, rather than write their answers. This exit ticket is also a preview of the next day’s lesson, so when I facilitate the whole class discussion, I will push students to use as many of the key terms from the classwork as they can.